Can a TCA Peel Tighten the Bags Under my Eyes?

TCA peels do nice at tightening skin creases under and around the eyes and usually need 3-4 peels at 2-3 week intervals for $350/peel but no nothing for the fat pads under the eyes protruding.  These need to be removed surgically.

TCA peels in the appropriate percentage (strength) and done with correct technique, can improve fine lines and can tighten the skin in the under eye area. There will be some downtime including redness, swelling and crusting, the severity of which will depend on the strength of the peel and the individual condition and skin type. I recommend you consult with a board-certified dermatologist or facial plastic surgeon experienced in using TCA to avoid any unwanted side effects. 

TCA will : 1. reduce fine lines and 2. tighten the skin somewhat. Larger lower eyelid bags may require a lower blepharoplasty (eyelid surgery) for more complete correction to: 1.Tighten and support the lower lid skin  2. remove or reposition the excess fat that is bulging and causing your bags. If done properly, dark circles can also be softened.

The bags under the eyes are herniated orbital fat, They do not improve with peels. Peels will improve the skin and fine wrinkles and pigmentation.
The bags are dealt with in several ways, the exact method will be determined after examining you. It could be fat injectiond, it could be fat distribution, and rarely removal of some of that fat and redistributing the rest of the fat